When I fix my paper for gum printing on a rigid substrate for re-registration, as I do for larger formats, I use a hot water bath to remove the print from the substrate, and this procedure necessitates varnishing it first, or otherwise part of the colour softens and dissolves in the hot water.
I use glossy or semi-matte varnish, and both definitely and considerably improve shadow values in particular, and the richness of colours. Therefore I think varnishing a gum print with an archival varnish is quite recommendable, and the same goes for iron-salt processes. I don't do it always, not even often, for it is quite extra work, and the character of the print certainly changes, but tonal values improve, and the print does not lose its hand-made quality.